Regularized Joint Estimation of Related Vector Autoregressive Models

In a number of applications, one has access to high-dimensional time series data on several related subjects. A motivating application area comes from the neuroimaging field, such as brain fMRI time series data, obtained from various groups of subjects (cases/controls) with a specific neurological disorder. The problem of regularized joint estimation of multiple related Vector Autoregressive (VAR) models is discussed, leveraging a group lasso penalty in addition to a regular lasso one, so as to increase statistical efficiency of the estimates by borrowing strength across the models. A modeling framework is developed that it allows for both group-level and subject-specific effects for related subjects, using a group lasso penalty to estimate the former. An estimation procedure is introduced, whose performance is illustrated on synthetic data and compared to other state-of-the-art methods. Moreover, the proposed approach is employed for the analysis of resting state fMRI data. In particular, a group-level descriptive analysis is conducted for brain inter-regional temporal effects of Attention Deficit Hyperactive Disorder (ADHD) patients as opposed to controls, with the data available from the ADHD-200 Global Competition repository.